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Funktsional. Anal. i Prilozhen., 2002, Volume 36, Issue 2, Pages 89–92 (Mi faa197)  

This article is cited in 27 scientific papers (total in 27 papers)

Brief communications

Fixed Points of Multivalued Contractions

P. V. Semenov

Moscow City Pedagogical University, Mathematical Department

Abstract: A fixed-point theorem is proved for a broad class of closed-valued $k(\;\cdot\;)$-contractions with $\limsup_{s\to t+0}k(s)<1$ for any positive $t$ and with $\limsup_{s\to0+0}k(s)=1$.

Keywords: multivalued contraction, fixed point, Reich's problem, $G$-summable function


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English version:
Functional Analysis and Its Applications, 2002, 36:2, 159–161

Bibliographic databases:

UDC: 517.988.52
Received: 30.11.2000

Citation: P. V. Semenov, “Fixed Points of Multivalued Contractions”, Funktsional. Anal. i Prilozhen., 36:2 (2002), 89–92; Funct. Anal. Appl., 36:2 (2002), 159–161

Citation in format AMSBIB
\by P.~V.~Semenov
\paper Fixed Points of Multivalued Contractions
\jour Funktsional. Anal. i Prilozhen.
\yr 2002
\vol 36
\issue 2
\pages 89--92
\jour Funct. Anal. Appl.
\yr 2002
\vol 36
\issue 2
\pages 159--161

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    This publication is cited in the following articles:
    1. Uderzo, A, “Fixed points for directional multi-valued k(center dot)-contractions”, Journal of Global Optimization, 31:3 (2005), 455  crossref  mathscinet  zmath  isi  scopus
    2. Eldred, AA, “On equivalence of generalized multi-valued contractions and Nadler's fixed point theorem”, Journal of Mathematical Analysis and Applications, 336:2 (2007), 751  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Semenov P.V., “On a contractivity condition in fixed point theory and the theory of selections”, Fixed Point Theory and its Applications, Banach Center Publications, 77, 2007, 239–245  crossref  mathscinet  zmath  isi
    4. Suzuki, T, “Mizoguchi-Takahashi's fixed point theorem is a real generalization of Nadler's”, Journal of Mathematical Analysis and Applications, 340:1 (2008), 752  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Benahmed S., Aze D., “On Fixed Points of Generalized Set-Valued Contractions”, Bulletin of the Australian Mathematical Society, 81:1 (2010), 16–22  crossref  mathscinet  zmath  isi  scopus
    6. Du W.-Sh., “Coupled Fixed Point Theorems for Nonlinear Contractions Satisfied Mizoguchi-Takahashi's Condition in Quasiordered Metric Spaces”, Fixed Point Theory Appl, 2010, 876372  mathscinet  zmath  isi
    7. Damjanovic B., Doric D., “Multivalued Generalizations of the Kannan Fixed Point Theorem”, Filomat, 25:1 (2011), 125–131  crossref  mathscinet  zmath  isi  elib  scopus
    8. Doric D., Lazovic R., “Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications”, Fixed Point Theory Appl, 2011, 1–8  mathscinet  adsnasa  isi
    9. Ciric L., Abbas M., Rajovic M., Ali B., “Suzuki Type Fixed Point Theorems for Generalized Multi-Valued Mappings on a Set Endowed with Two B-Metrics”, Appl. Math. Comput., 219:4 (2012), 1712–1723  crossref  mathscinet  zmath  isi  elib  scopus
    10. Repovs D., “A Two-Parameter Control for Contractive-Like Multivalued Mappings”, Topology Appl., 159:7, SI (2012), 1899–1905  crossref  mathscinet  zmath  isi  elib  scopus
    11. Abbas M., Ali B., Vetro C., “A Suzuki Type Fixed Point Theorem for a Generalized Multivalued Mapping on Partial Hausdorff Metric Spaces”, Topology Appl., 160:3 (2013), 553–563  crossref  mathscinet  zmath  isi  elib  scopus
    12. Abbas M., Ali B., “Fixed Point of Suzuki-Zamfirescu Hybrid Contractions in Partial Metric Spaces via Partial Hausdorff Metric”, Fixed Point Theory Appl., 2013, 21, 1–16  crossref  mathscinet  isi  scopus
    13. Popescu O., “A New Type of Contractive Multivalued Operators”, Bull. Sci. Math., 137:1 (2013), 30–44  crossref  mathscinet  zmath  isi  elib  scopus
    14. Kumam P., Aydi H., Karapinar E., Sintunavarat W., “Best Proximity Points and Extension of Mizoguchi-Takahashi's Fixed Point Theorems”, Fixed Point Theory Appl., 2013, 242  crossref  mathscinet  zmath  isi  scopus
    15. Semenov P.V., “On Contraction-Type Assumptions Avoiding the Hausdorff Distance”, Topology Appl., 160:11, SI (2013), 1237–1240  crossref  mathscinet  zmath  isi  elib  scopus
    16. S. R. Gajnullova, T. N. Fomenko, “Functionals Subordinate to Converging Series and Some Applications”, Math. Notes, 96:2 (2014), 294–297  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    17. Abbas M., Ali B., Petrusel G., “Fixed Points of Set-Valued Contractions in Partial Metric Spaces Endowed With a Graph”, Carpathian J. Math., 30:2 (2014), 129–137  mathscinet  zmath  isi
    18. Semwal P., Dimri R.Ch., “A Suzuki Type Coupled Fixed Point Theorem For Generalized Multivalued Mapping”, Abstract Appl. Anal., 2014, 820482  crossref  mathscinet  isi  elib  scopus
    19. Fomenko T.N., “Approximation Theorems in Metric Spaces and Functionals Strictly Subordinated To Convergent Series”, Topology Appl., 179:SI (2015), 81–90  crossref  mathscinet  zmath  isi
    20. T. N. Fomenko, “Browder functions and theorems on fixed points and coincidences”, Izv. Math., 79:5 (2015), 1087–1095  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    21. Abbas M., Ali B., Butt A.R., “Existence and Data Dependence of the Fixed Points of Generalized Contraction Mappings With Applications”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 109:2 (2015), 603–621  crossref  mathscinet  zmath  isi  elib  scopus
    22. Jleli M., Nashine H.K., Samet B., Vetro C., “on Multivalued Weakly Picard Operators in Partial Hausdorff Metric Spaces”, Fixed Point Theory Appl., 2015, 52  crossref  mathscinet  zmath  isi  elib  scopus
    23. Kumam P., Nguyen Van Dung, Sitthithakerngkiet K., “a Generalization of Ciric Fixed Point Theorems”, Filomat, 29:7 (2015), 1549–1556  crossref  mathscinet  zmath  isi  elib  scopus
    24. Sintunavarat W., Kumam P., “Best Proximity Points Theorems For Generalized Mizoguchi-Takahashi'S Contraction Pairs”, J. Nonlinear Convex Anal., 17:7, SI (2016), 1345–1361  mathscinet  zmath  isi
    25. Suzuki T., “Basic Inequality on a B-Metric Space and Its Applications”, J. Inequal. Appl., 2017, 256  crossref  mathscinet  zmath  isi  scopus
    26. Ali B., Abbas M., “Existence and Stability of Fixed Point Set of Suzuki-Type Contractive Multivalued Operators in B-Metric Spaces With Applications in Delay Differential Equations”, J. Fixed Point Theory Appl., 19:4 (2017), 2327–2347  crossref  mathscinet  zmath  isi  scopus
    27. B. D. Gelman, “Neravenstvo Karisti i $\alpha$-szhimayuschie otobrazheniya”, Funkts. analiz i ego pril., 53:3 (2019), 84–88  mathnet  crossref  elib
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